Crossed Fields

Electron_deflection.jpged Fields
Crossed fields are created by crossing uniform electric and magnetic fields.

In 1897, J.J Thompson was able to measure the specific charge on an electron (e/m) by crossing uniform electric and magnetic fields. The crossing of the fields was used to deflect electrons with equal and opposite forces. To provide an electrical force (Fe) and a magentic force (Fm) which are both in balance, there are two parallel metal plates providing the electrical force and Helmholtz coils are used to provide the magnetic force.]

Equations of crossed fields
So the Force of the electrical field is equal to the magnetic field and can be equated as so:

FE=FM so Electrical field strength x Electron charge = Magnetic flux density x electron charge x Voltage (Ee=BeV)

Cancelling the charge on the electron of e gives:

Velocity =Electrical field strength over Magnetic flux density (V=E/B)

As with the fine beam tube the electron is acclerated by the voltage between the anode and the cathode so the kinetic energy is given by:

velocity = square root of 2(e/m)Voltage

So this equation is also equal to E(2)/B(2)= 2(e/m)V

This then gives the ratio of charge on an electron (e/m) = E(2)/2VB(2)

The equation can be simplified when the voltage across the parallel plates is equal to the voltage between the anode and the cathode.

This means that Electrical field strength (E=V/d) can be used to modifiy the equation for (e/m) to:

e/m= Voltage/2(distance(2))(Magnetic flux density(2))

e/m=V/2d(2)B(2)